One day, I could download some of my allotted photos to computer just fine. Now, they all want to only open in Ps using cloud, which I don't want to bother with - So now I can't license the rest of my photos!

Not sure exactly what is happening. You should be able to license images without any programs at all? I am confused though as your title says downloading images but your question is about licensing. Can you be a bit more specific on steps you are taking? Screenshots also help to see if it is something you are doing wrong.

I think I figured it out. It seems certain images aren’t in JPEG format, they are in AI or other formats I don’t use. The image I downloaded to my computer was AI, and once I went back and forth several times to try it and I realized that was why I couldn’t open it realized I need to look at the image format before downloading to make sure it is a jpeg. But it was directing me to download apps for various publishing programs, which I’m not interested in and that was confusing me. Is there a way to “return” it to my allotment as I don’t intend to use illustrator any time soon?